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MathNet 2024-part-03 — 168 problems (EN–VI) Question 108

Math Olympiad Vault · MathNet 2024-part-03 — 168 problems (EN–VI)

Question 108

Suppose $f(x)$ and $g(x)$ are quadratic trinomials with the property that
$$
\frac{f(-2)}{g(-2)} = \frac{f(3)}{g(3)} = 4.
$$
Given that $g(5) = 2$, $f(7) = 8$, and $g(7) = 6$, determine the value of $f(5)$.